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Background <p>As a promising cross-sea infrastructure, the submerged floating tunnel (SFT) relies on anchor cables as its primary load-bearing components, with their dynamic response critically influencing the overall safety and feasibility of the system. Existing studies often employ simplified mechanical models and solution methods, which may fail to accurately capture the nonlinear vibration characteristics of anchor cables.</p> Purpose <p>To overcome this limitation, this paper develops a precise and general analytical framework for analyzing the nonlinear vibration of anchor cables, enabling efficient and accurate determination of their free vibration response.</p> Method <p>First, a Bernoulli–Euler beam model with shallow sag is used to establish the dynamic equation of the anchor cable, incorporating elastic support boundary conditions. Next, the dynamic stiffness method (DSM) is combined with the perturbation method to accurately compute the modal frequencies and mode shapes. Finally, the energy equivalence principle is applied to decouple the nonlinear equations of motion, leading to an analytical solution for the dynamic response.</p> Results and Discussion <p>Numerical results confirm that including the first seven modes provides a more accurate representation of the cable's dynamic behavior. The maximum displacement along the cable occurs near its trisection points, while the maximum stress is located close to the upper anchorage. Both the fluid damping coefficient and the structural damping ratio significantly affect the vibration attenuation. The proposed method demonstrates higher computational accuracy and efficiency compared to conventional numerical approaches, effectively balancing analytical precision with engineering practicality.</p>

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Nonlinear Vibration of Marine Anchor Cables Using Dynamic Stiffness Method-Perturbation Method

  • 期刊论文

  • 发表日期：

    2026年1月7日

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  • Han Fei,
  • Sun Linfei,
  • Wu Lei,
  • Deng Zichen

摘要

Background

As a promising cross-sea infrastructure, the submerged floating tunnel (SFT) relies on anchor cables as its primary load-bearing components, with their dynamic response critically influencing the overall safety and feasibility of the system. Existing studies often employ simplified mechanical models and solution methods, which may fail to accurately capture the nonlinear vibration characteristics of anchor cables.

Purpose

To overcome this limitation, this paper develops a precise and general analytical framework for analyzing the nonlinear vibration of anchor cables, enabling efficient and accurate determination of their free vibration response.

Method

First, a Bernoulli–Euler beam model with shallow sag is used to establish the dynamic equation of the anchor cable, incorporating elastic support boundary conditions. Next, the dynamic stiffness method (DSM) is combined with the perturbation method to accurately compute the modal frequencies and mode shapes. Finally, the energy equivalence principle is applied to decouple the nonlinear equations of motion, leading to an analytical solution for the dynamic response.

Results and Discussion

Numerical results confirm that including the first seven modes provides a more accurate representation of the cable's dynamic behavior. The maximum displacement along the cable occurs near its trisection points, while the maximum stress is located close to the upper anchorage. Both the fluid damping coefficient and the structural damping ratio significantly affect the vibration attenuation. The proposed method demonstrates higher computational accuracy and efficiency compared to conventional numerical approaches, effectively balancing analytical precision with engineering practicality.